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Spatial variance is an important characteristic of spatial random variables. It describes local deviations from average global conditions and is thus a proxy for spatial heterogeneity. Investigating instability in spatial variance is a useful way of detecting spatial boundaries, analysing the internal structure of spatial clusters and revealing simultaneously acting geographic phenomena. Recently, a corresponding test statistic called ‘Local Spatial Heteroscedasticity’ (LOSH) has been proposed. This test allows locally heterogeneous regions to be mapped and investigated by comparing them with the global average mean deviation in a data set. While this test is useful in stationary conditions, its value is limited in a global heterogeneous state. There is a risk that local structures might be overlooked and wrong inferences drawn. In this paper, we introduce a test that takes account of global spatial heterogeneity in assessing …